A QBD Approach To Multi-Population Evolutionary Games

Evolutionary Game Theory is an important research branch that has seized an increasingly significant share in Economics. It aims at explaining a population's aggregate behavior pattern under evolutionary or learning mechanisms, and has considerable potential for modeling a lot of substantive issues in the fields such as biology, economics and management science.This research first aims at the class of evolutionary game models with two populations, and proposes a unified modeling framework as well as an effective algorithm for solving Evolutionarily Stable Strategy (ESS). The approach is: modeling evolutionary games by constructing corresponding Quasi-Birth-Death (QBD) processes, and then calculating the limit probabilities of the QBD processes by means of RG-factorization algorithms. Based on this technique, this research scrutinizes the following three types of evolutionary game models with two populations: (1) two independent populations with each embedded with a 2×2 symmetric stage game, (2) two interactive populations with each embedded with a 2×2 symmetric stage game and with interactive strategy dependancey factor, and (3) two interactive populations whose interaction can be modeled by a 2×2 asymmetric stage game. This research then provides numerical examples for demonstrating the modeling framework and algorithm, and also discusses the influences of different modeling parameters and stage game payoff matrix on ESS.The research finally generalizes the above technique to Multi-Population Evolutionary Game Models. We propose an iterative construction method for constructing corresponding QBD processes for multi-population evolutionary game models. In a word, this research has proposed an applicable modeling and solving framework for evolutionary game models with arbitrary finite number of populations.